Question: Write the equation of a line that is perpendicular to $x=3$ and that passes through the point $(0,-4)$.
Explanation: Getting started Key idea: The slopes of perpendicular lines are negative reciprocals of each other. Step 1: Find the slope Lines with the form of $x=c$ are vertical lines, which means that their slopes are undefined. Lines perpendicular to vertical lines are horizontal lines, which have a slope of $0$. Since the given line is vertical, the slope of its perpendicular line is $0$. Step 2: Substitute the known point into linear equation The perpendicular line will have a slope of $C{0}$ and pass through the point ${(0,-4)}$. Let's start from the point-slope form of the equation of the perpendicular line, then solve for $y$. [What is the point-slope form?] $\begin{aligned} y-{(-4)} &= C{0}(x-{0})\\\\\\ y+4 &= 0 \\\\\\ y &= {-4} \end{aligned}$ Answer $y={-4}$. ${2}$ ${4}$ ${6}$ ${8}$ ${\llap{-}4}$ ${\llap{-}6}$ ${\llap{-}8}$ ${2}$ ${4}$ ${6}$ ${8}$ ${\llap{-}4}$ ${\llap{-}6}$ ${\llap{-}8}$ $y$ $x$